ATWOOD OCEANICS, INC. 2013 LONG-TERM INCENTIVE PLAN TERMS AND CONDITIONS OF NON-EMPLOYEE DIRECTOR RESTRICTED STOCK UNIT AWARD

Exhibit 10.5

[Date]

TO:

FROM:

Atwood Oceanics, Inc. (the “Company”) hereby awards to you, effective as of [Date] (the “Date of Grant”),                  restricted stock units (“Restricted Stock Units”) evidencing the right to receive an equivalent number of shares of Common Stock, $1.00 par value, of the Company, subject to adjustment as provided in Section 11 of the Atwood Oceanics, Inc. 2013 Long-Term Incentive Plan (the “Plan”).

Except as otherwise provided in Section 2 of the Terms and Conditions of Non-Employee Director Restricted Stock Unit Award, attached hereto as Appendix A (the “Terms and Conditions”), the Restricted Stock Units will vest in substantially equal installments on each monthly anniversary of the Date of Grant (each a “Vesting Date”) during the twelve month period beginning on of the Date of Grant; provided you remain a director of the Company on each applicable Vesting Date.

The award of Restricted Stock Units is governed by the terms and conditions of the Plan, any rules and regulations adopted by the Compensation and Human Resources Committee of the Board of Directors of the Company, and the Terms and Conditions which form a part of this award letter to you (the “Notice”).

Appendix A

ATWOOD OCEANICS, INC.

2013 LONG-TERM INCENTIVE PLAN

TERMS AND CONDITIONS OF

NON-EMPLOYEE DIRECTOR RESTRICTED STOCK UNIT AWARD

The restricted stock units (the “Restricted Stock Units”) awarded to you on the “Date of Grant” set forth in the award letter to you (the “Award Letter”) by Atwood Oceanics, Inc. (the “Company”) are subject to the 2013 Long-Term Incentive Plan (the “Plan”), these Terms and Conditions and any rules and regulations adopted by the Committee. Terms used herein and not otherwise defined shall have the meaning set forth in the Plan and the Award Letter.

1. Vesting/Forfeiture. Except as otherwise accelerated pursuant to Section 2 below, the Restricted Stock Units shall vest in substantially equal installments on each monthly anniversary of the Date of Grant (each a “Vesting Date”) during the twelve month period beginning on of the Date of Grant (the “Restriction Period”). If your service as a director of the Company terminates for any reason, any unvested Restricted Stock Units shall be automatically forfeited on the date of your termination of service.

2. Change of Control. Notwithstanding the provisions of Section 1 of these Terms and Conditions, in the event of a Change of Control, the unvested Restricted Stock Units shall automatically vest and the Restriction Period shall terminate.

3. Settlement and Delivery of Common Stock. Settlement of vested Restricted Stock Units shall be made no later than 15 days after the earlier of (i) termination of the Restriction Period or (ii) the date of your separation of service. In the event of vesting pursuant to Section 2, the Restricted Stock Units shall be settled no later than 15 days after the Change of Control. In addition, upon the date of delivery of shares of Common Stock in settlement of Restricted Stock Units, you shall also be entitled to receive a lump sum cash payment equal to the Dividend Equivalent Amount. Notwithstanding the foregoing, the Company shall not be obligated to issue any shares of Common Stock if counsel to the Company determines that such sale or delivery would violate any applicable law or any rule or regulation of any governmental authority or any rule or regulation of, or agreement of the Company with, any securities exchange or association upon which the Common Stock is listed or quoted. The Company shall in no event be obligated to take any affirmative action in order to cause the issuance of shares of Common Stock to comply with any such law, rule, regulation or agreement. For purposes of this award of Restricted Stock Units, “Dividend Equivalent Amount” means the sum of all cash dividends, if any, declared on shares of Common Stock you receive in settlement of Restricted Stock Units where the record date is after the Date of Grant, but prior to the date such shares of Common Stock are distributed to you.

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4. Transferability. You may not sell, transfer, pledge, exchange, hypothecate, or otherwise dispose of the Restricted Stock Units prior to settlement under Section 3.

5. Rights as Shareholder. You shall not be entitled to any of the rights or privileges of a shareholder of the Company in respect of any shares of Common Stock unless and until the Restricted Stock Units have been settled by the issuance of Common Stock to you. If, from time to time during the Restriction Period, there is any capital adjustment affecting the outstanding Common Stock as a class without the Company’s receipt of consideration, the Restricted Stock Units shall be adjusted in accordance with the provisions of Section 11 of the Plan.

6. Plan Governs. The Restricted Stock Units and the Notice are subject to all of the terms and conditions of the Plan, except that no amendment to the Plan shall adversely affect your rights under the Notice. All the terms and conditions of the Plan, as may be amended from time to time, and any rules, guidelines and procedures which may from time to time be established pursuant to the Plan are hereby incorporated into the Notice. In the event of a discrepancy between the Notice and the Plan, the Plan shall govern.

7. Withholding. Upon settlement of the Restricted Stock Units, the market value of the shares on the date of settlement will be included with all other compensation paid during the year for services performed and reported on Internal Revenue Service Form 1099. You will be responsible for payment of all income taxes assessable on the Restricted Stock Unit Award.

8. Code Section 409A; No Guarantee of Tax Consequences. The award of Restricted Stock Units is intended to be (i) exempt from Section 409A of the Code (“Section 409A”) by compliance with the short-term deferral exemption as specified in Treas. Reg. § 1.409A-1(b)(4); or (ii) in compliance with Section 409A, and the provisions of the Notice will be administered, interpreted and construed accordingly. Notwithstanding the provisions of Section 2 of these Terms and Conditions, in the event of a Change of Control that does not meet the requirements of Treas. Reg. §1.409A-3(i)(5), any amounts that would otherwise be payable hereunder as nonqualified deferred compensation within the meaning of Section 409A shall be fully vested but shall be settled on the twelve month anniversary of the Date of Grant. To the extent required to comply with Section 409A, you shall be considered to have terminated service with the Company when you incur a “separation from service” with the Company within the meaning of Section 409A(a)(2)(A)(i) of the Code. The Company makes no commitment or guarantee to you that any federal or state tax treatment will apply or be available to any person eligible for benefits under the Notice.

9. Governing Law. The Plan and the Notice shall be governed by, and construed in accordance with, the laws of the State of Texas, without regard to conflicts of laws. The courts in Harris County, Texas shall be the exclusive venue for any dispute regarding the Plan or the Notice.

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